# Workgroup Convex and Integral Geometry

The workgroup *Convex and Integral Geometry* is now part of the research group Spatial Stochastics and Stochastic Geometry.

# Research

Research Interests - Projects - Cooperations - Publications (since 2004)

The focus of the research of the group is on Convex Geometry, Integral Geometry and Stochastic Geometry. Convex and Integral Geometry are connected to various mathematical disciplines such as functional analysis, optimization and discrete geometry, and in particular to Stochastic Geometry. Classical Integral Geometry investigates integral averages of geometrically relevant functionals with respect to the full motion group. The stochastic modelling of problems coming from applications motivates the study of more general groups of transformations. In particular, this leads to translative integral geometry. In the context of Convex Geometry, these developments correspond to the investigation of new geometric functionals. A central topic in the research of this workgroup are geometric and functional inequalities and related stability results. Another key aspect is the analysis of inverse geometric problems. Information about a geometric object is often available only in the form of an integral transform, or in terms of information about projections or sections of the object. Therefore an important task is the determination and reconstruction of information about the original object itself. Geometric results are also required in investigations of the group in the context of Stochastic Geometry, in particular in the analysis of geometric point processes, random tessellations and random polytopes.

Members of the group regularly offer courses on Convex Geometry, Integral Geometry and Stochastic Geometry. These courses are complemented by student's seminars and lectures provided in the framework of the workgroup on Stochastic Geometry.